Question

The potential energy of a particle under a conservative force is given by $U\left(x\right)=\left(x^{2} - 3 x\right) \, J$ . The equilibrium position of the particle is at $x \, m$ . The value of $10x$ will be

Answer 1

$U\left(x\right)=\left(x^{2} - 3 x\right)J$
For a conservative field, Force, $F =-\frac{d ⁡ U ⁡}{d ⁡ x}$
$\therefore F =-\frac{d ⁡}{d ⁡ x}\left(x^{2} - 3 x\right)=-\left(2 x - 3\right)=-2x+3$
At equilibrium position, $F=0$
$-2x+3=0\Rightarrow x=\frac{3}{2}m =1\cdot 5\text{m}$